Casey (Krysta Rodriguez) and Aaron (Zachary Levi) get on track together in a new musical.Joan Marcus

By the end of Broadway’s “First Date,” Zachary Levi has won over the entire audience — you can feel everybody, women and men, young and old, swooning. If someone happened to smuggle in a small dog, you can bet it would go gaga over him, too.

He’s so remarkably at ease, it’s hard to believe the show — about a date unfolding in real time — marks his professional theater debut. And a singing one at that.

Levi spent five seasons as the star of the action-comedy series “Chuck,” in which he played a computer nerd who stumbles onto covert operations. His part here isn’t entirely dissimilar in spirit.

Levi’s Aaron is a gawky, likable corporate banker who’s been set up on a blind date by a colleague. This makes Aaron uncomfortably nervous, but he gamely trundles through, allowing Levi to set a new standard for adorkableness.

The show’s book, by Austin Winsberg (“Gossip Girl,” “Jake in Progress”), is neatly efficient. Aaron meets Casey (Krysta Rodriguez) at a restaurant, where their fellow diners and the waiter, changing costumes and personas at the drop of a hat, provide a kind of Greek chorus, alongside imaginary interventions from friends and family members.

But while Levi quickly wins us over, it’s harder to root for Rodriguez’s relentlessly caustic Casey.

The role is a tough one because Casey is such a cliché: the walking wounded hiding behind a cool, blasé exterior. “We both know that all this bravado is really just you being afraid of getting hurt,” her sister, Lauren (Sara Chase), tells her.

Just in case we still don’t get the message, Casey has a whole song, “Safer,” that explains how she uses sarcasm to protect herself from disappointment.

Rodriguez made a fine Wednesday in Broadway’s “The Addams Family,” but here she just duplicates her brittle performance as Katharine McPhee’s roommate, Ana, on TV’s “Smash.” She’s just not likable enough to make us overlook Casey’s rudeness.

But the show really rests on Levi’s shoulders — and he carries it effortlessly.

The only clue we had that he could carry a tune was from his duet with Mandy Moore in Disney’s “Tangled.” Here, he turns out to be able to do far more than just sing a song: He can sell it. His 11 o’clock number, “In Love With You,” is a tour de force of comic timing, physical clowning and effective interpretation.

A loving relationship does come out of “First Date,” but it’s not between Aaron and Casey — it’s between Zachary Levi and theater. And it will last.